I really like everything Arolinecay wrote, but just wanted to add my .02!
Even someone who is really comfortable with Sudbury can have moments of "Oh no, is this the right thing to do???" I've talked about it with other parents of students at the school my dk go to, and we all agree that it is often scary. I believe the reason for that is trust. It is so hard to trust that your kids are going to figure things out, learn to read, to write, to do math, to live in the world, to be ok. I think that regular schooling can take a lot of that pressure off of you, because someone else is helping out with that stuff. Plus, if you send your kids to a Sudbury school, I can guarantee you will get tons of pressure from everyone (your family, friends, almost everyone you have explained the model to...).
It is hard to trust a little kid to know what is right for them--they seem so innocent and oblivious. They have random urges that they just...follow! It's a given in our society that this is not a good thing, that kids are evil (I swear, some people seem to think that!) or at the very least self-destructive. While I do agree that some urges need to be stopped (crossing the street anytime you feel like it, instead of looking for cars), most of the other ones are up for interpretation.
A kid at a Sudbury school is going to learn how to read and write and how to do math, simply because you need these skills to do all kinds of interesting things. My daughter learned to read so she could play video games without having to have someone else to read directions and character dialogue (and now she spends hours reading every day). Kids learn how to do math so they know how much they can spend on candy, or how to add/divide/subtract points in games, or to play cards. Some kids learn how to do those things because of much loftier reasons, but other kids just want to read Captain Underpants.
As for the other subjects, they aren't going to learn them all. Anatomy? Probably not, unless it sparks their interest beyond body parts (most people just figure those out from everyday use...a kid is crying because they hurt their tailbone, or they get an ear infection and the doctor explains the anatomy of the ear to them). History I would imagine would be more likely, simply because there are a lot of fascinating things that happened in the past. But their knowledge won't necessarily be complete. Maybe they will know a lot of the history of the Civil War, but not much about the French-Indian War (I went to both Catholic School and public school, and I don't remember anything about that one either, aside from the name...).
Again it is about trust, but also what you ultimately want for your kids. I personally don't think anyone is all that well-rounded, and I would prefer my kids to have had a chance to follow their passions and have the inner strength to do things on their own than to have a passing knowledge of a hundred subjects, 95 of which they associate with boredom.
-cloudspinning